Iimpawu logarithm, okanye emangalisayo - ecaleni ...

Isidingo computing wabonakala buqu kwaoko, kamsinya nje wayekwazi ubungakanani izinto ngeenxa zonke kuye. Kokuba kucingelwa ukuba uvandlakanyo logic oluninzi zenza ukuba kancane "add-thabatha 'imfuno uhlobo ukubala. La manyathelo ezimbini ezilula ekuqaleni ezingundoqo - zonke ezinye zazo amanani eyaziwa-phinda, hlula, exponentiation , njl - i "ngoomatshini" ilula kwezinye ubuchule azo, ezo zisekelwe izibalo ezilula - "goca-thabatha". Nantoni na, kodwa nokudalwa algorithms ukuba becomputing yeyona mpumelelo inkulu yokucinga, kunye nababhali babo ngonaphakade ushiye uphawu zabo kwimemori uluntu.

Ezintandathu okanye ezisixhenxe kwiinkulungwane ezadlulayo endle yeNavigeyishini lwaselwandle ngeenkwenkwezi kwandise imfuneko izixa ezikhulu izibalo, nto leyo akumangalisi, kuba kwakusazeka ukuba ngamaXesha Aphakathi uphuhliso navigation kunye neenkwenkwezi. Ukuhlala kugcinwe lo ibinzana elithi "imfuno ukwandisa unikezelo" eliqela zezibalo sacinga - ukubuyisela kakhulu ekusekweni kwemisebenzi yabo Ekwandeni ezimbini kwamanani alula Ukongeza (abahlaselwe luthathwa ingcamango indawo hlula yi nokukhupha). Angokokusebenza nenguqulo entsha becomputing inkqubo nechazwe 1614 kumsebenzi Dzhona Nepera ne kunene emangalisayo kwesihloko "Inkcazelo ezimangalisayo kwetafile see logarithm." Kakade ke, ukuphucuka inkqubo entsha yaqhubeka ixesha elide, kodwa iimpawu ezingundoqo see logarithm eyayichazwe ngaphezulu Napier. Ingcamango yokubala inkqubo usebenzisa logarithm kukuba ukuba uthotho amanani enza ukuqhubela zejometri, see logarithm zabo nazo zenze ukuqhubela phambili, kodwa arithmetic. Phambi pre-yenzelwe amacwecwe entsha indlela yokuvumelana lula izibalo, kwaye yokuqala slide rule (1620 ngonyaka) Mhlawumbi kuqala yamandulo kakhul wokubala - ebalulekile lobunjineli isixhobo.

Ngokuba imigodi ngxi endleleni isoloko. Ekuqaleni, lo logarithm ye isiseko athathiweyo ngempumelelo kwaye ukuchaneka ukubala kangako, kodwa sele ngo-1624 itafile esulungekisiweyo kunye nesiseko wokugqibela ziye zapapashwa. Iimpawu logarithm zivela ungaphinda kumiselwa: logarithm ye b - C linani apho, xa iqondo kwesiseko logarithm (inombolo A), nto leyo eziliqela b. Classic ushicilelo khetho sijongeka: logą (b) = C - ukuba afundeka ngolu hlobo: b logarithm, kwi siseko A, kukuthi inani C Ukuze ukwenza intshukumo usebenzisa kuba yinto eqhelekileyo, logarithm inombolo, kufuneka wazi uluhlu lwemithetho, owaziwa njenge "iipropati logarithm. " Enyanisweni, yonke imithetho babe subtext eqhelekileyo - ukongeza njani, uthabathe uze ukuguqula logarithm. Ngoku siyazi indlela yokuyenza.

zero lwe logarithm olusezantsi kunye enye

1. logą (1) = 0, i logarithm ye inani 1 ilingana no0 ngenxa yaso nasiphi na isizathu - Njengesiphumo esithe ngqo kukho inani kuvuselwa isidanga zero.

2. logą (A) = 1, i logarithm efanayo kunye nenombolo base-1 - yaziwa kakuhle oyinyaniso naliphi na inani ngamandla yokuqala.

Ukudibanisa nokuthabatha see logarithm

3. logą (m) + logą (n) = logą (m * n) - isixa see logarithm i logarithm yamanani eziliqela emsebenzini.

4. logą (m) - logą (n) = logą (m / n) - umahluko logarithm amanani, efana odlulileyo, lilingana logarithm ye umlinganiselo kula manani.

5. logą (1 / n) = - logą (n), i logarithm ye unikezelo lwe logarithm kule nombolo ilingana no 'thabatha'. It Kulula ukubona ukuba lo kukuthi result odlulileyo ibinzana 4 ngenxa m = 1.

Kulula ukuba uqaphele ukuba imithetho ifuna 3-5 kumacala omabini ye log neziqu ezifanayo.

Izalathi ngo lwe logarithm olusezantsi ngokoMthetho

6. logą (mn) = n * logą (m), i logarithm ye inani isidanga n i logarithm ye eli nani liphindaphindwe isalathi n.

7. log (IZe) (b) = (1 / c) * logą (b), othi "logarithm ye b, ukuba isiseko na uhlobo Mseb, na imveliso logarithm ukuya isiseko b A kunye nenani reverse c».

Formula utshintsha base logarithm

8. logą (b) = - logC (b) / logc (A), i logarithm ye inani b ukuya kwisiseko A kwi inguqu kwi siseko C zibalwe QUOTIENT lwe logarithm ukuya kwisiseko b kunye logarithm nenombolo isiseko elingana edlulileyo kwesiseko A, kwaye nomqondiso "thabatha".

Le nkqubo ingentla iya logarithm kunye zazo neempawu ukuvumela efanelekileyo isicelo lula ukubala olukhulu amanani kwimiboniso, oku kunciphisa ixesha lwamanani izibalo kunye inikezela elikholekileyo ngokuchanekileyo.

Akumangalisi ukuba kwinzululwazi nobunjineli iimpawu see logarithm zisetyenziselwa imbonakaliso ezininzi zendalo ophathekayo. Umzekelo, eyaziwa ukusebenzisa amaxabiso isalamane - decibels xa kulinganiswa exubileyo nokukhanya physics, ubukhulu ngokupheleleyo ngeenkwenkwezi kwi pH in chemistry kunye nabanye.

lula intelekelelo ukusebenza lwe logarithm olusezantsi khangela ukuba sithathe, umzekelo, kwaye sanda inani elinemivo ezintlanu 3 "ngesandla" (in a column), esebenzisa iitafile see logarithm kwi ephepheni kunye rule slide. Kwanele ukuba nithi ukuthi ngasekupheleni kwimeko, ukubala izakuthatha amandla ka 10 imizuzwana Yintoni eyona nto singamangaliswa yinto yokuba kule mihla calculator ezi zibalo ngokuthabatha ixesha, engekho ngaphantsi.